Operations and Algebraic Thinking

Generate and analyze patterns.

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Resource | Resource Type Grade Level | Rating |
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This three-part interactive lesson has students use spatial sense and analytical skills to investigate the parts of three-dimensional polyhedra. Students view and control animations of the solids and their nets, which help them to count faces, edges and vertices, and to establish Euler's relation among those counts. Teachers notes, worksheets and printable nets are provided. | Activity, Interactive Media Grade Level: 4, 5, 6+ | |

This 75-page pdf document demonstrates the connections between the CCSS content standards and the mathematical practice standards. It is a compilation of research, standards from several states, instructional strategies, common misconceptions, and examples for each standard at the grade 4 level. It is intended to help teachers understand what each standard means in terms of what students must know and be able to do. Additional flip books are cataloged separately for grades K-3 and 5. | Instructional Strategy, Reference Materials Grade Level: 4 | |

This web page provides links to resources aligned to the CCSS that guide and support fourth grade mathematics teaching and learning. Tasks developed by the Mathematics Assessment Resource Service (MARS) for the Noyce Foundation, Problems of the Month, (POM home page is cataloged separately) and videos of public lessons and number talks developed by the Noyce Foundation are also included. The performance tasks were originally designed to measure students' ability to solve non-routine problems and then to explain and justify their solutions. The task scoring rubric, student responses, and discussion of student understanding and misconceptions are provided to improve instruction. Resources are listed for specific grade 4 standards and are also organized by progression for an alternate search route. | Activity, Instructional Strategy, Problem Set, Reference Materials, Video Grade Level: 4 | |

This page provides examples of 4th Grade Number (Operations and Algebraic Thinking, Number and Operations in Base Ten, and Number Operations-Fractions) activities aligned with the Common Core State Standards. A CCSS standard is stated and the possible activities are listed below and linked. All activities are suitable for use in Math Centers, small group or whole class settings and are designed to elicit a range of responses and provide opportunities for students to communicate their reasoning and mathematical thinking. Instructions for each task are typed in large print and written in child-friendly language to enable students to work on activities independently after a brief introduction to the task. All files for the 4th Grade Number Activities listed are in PDF format. | Activity, Game Grade Level: 4 | |

This problem reinforces the telling of time on a digital clock, and it requires students to work systematically. The number of 'times' the digit 5 appears in a 24-hour period is a matter of a solver's assumptions. Ideas for implementation, extension and support are included along with a printable poster. A link to an interactive Class Clock (cataloged separately) is provided. | Activity Grade Level: 3, 4, 5 | |

This Technology Problem of the Week (tPoW) challenges students to compile a spreadsheet that tracks different savings rates across different time spans, and to then use their accounting work to identify the calendar date when those contributions reach the goal of accumulating 1,000,000 pennies. Solve and explain your solution; download hints and answer checks. Also available in Spanish. Free registration is required. | Problem Set Grade Level: 4, 5 | |

This 1-minute video created by the UK Department of Education as an algebra lesson starter is based around how many friends can sit at a birthday party table. The video shows the birthday boy and girl sitting at opposite ends of the table with their guests sitting two on either side. As more tables are added and the number of children grow, a pattern starts to appear. Children are asked to predict how many children could come to the party if there were 100 tables. | Instructional Strategy, Video Grade Level: 3, 4, 5 | |

This web site contains information and interactive applets related to our Hindu-Arabic number system. Users learn the history and structure of the system as well as how to count and write numbers. Users can learn and practice various algorithms for whole number computation and explore fractions, decimals and percents in our number system. The site explains various sets of numbers and how they relate to operations. | Activity, Interactive Media, Tutorial, Reference Materials Grade Level: 1, 2, 3, 4, 5 | |

This interactive Java applet helps students learn about sequences and patterns through analysis of attributes. The user analyzes the existing pattern and must complete the "train" by dragging the appropriate shapes into place. The user is required to discern which attribute is used to create the pattern (color, shape, or number) as well as determine how to extend it. | Activity, Interactive Media Grade Level: 2, 3, 4 | |

In this formative assessment lesson students identify patterns (both linear and exponential) in a realistic context. They may solve this problem through a variety of strategies, providing opportunities for groups of students to share and critique various problem solving approaches. | Activity, Lesson Plans Grade Level: 4, 5, 6+ |